When you say he's floating vertically, do you mean with his nose to the surface? Is he gasping for air? Is he able to swim down, or does he seem to be stuck at the top? Also, do you have a thermometer and a liquid test kit? I really don't know what your climate is like right now, but most sick bettas will just not get better if it is too cold. You said you put him in a smaller container, what is your water change schedule on it? Personally, I would move him back into his original container because a larger container means less frequent water changes because the increased water volume takes longer to build up waste. This means less stress for your already compromised betta.
As for feeding him, he really needs a good staple of betta pellets or flakes, but being sick he may not ever eat them. At any rate, whatever you are feeding him needs to be fed every day. If however, he does seem bloated fasting him for a day will probably help.
The answers to the questions above, along with your water test readings (if you don't have a test kit you can bring some water to the pet store and ask them to test it for you, just make sure they give you actual numbers not just "fine") will help us to diagnose the problem.